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For symbolic computation: ASTs, mathematical expressions, code that manipulates code structure, expression transformations.
Codex または Claude でインストール この Prompt をコピーして Codex、Claude、または他のアシスタントに貼り付けると、Skill ページを確認してインストールできます。
SOC 職業分類に基づく
Conducts iterative deep research on any topic using web search, progressive exploration, and structured synthesis. Use when asked for comprehensive research, deep investigation, thorough analysis, or multi-source exploration of any topic. Triggers: research, investigate, deep dive, comprehensive analysis, explore thoroughly, find everything about.
For cross-cutting concerns: add behavior without modifying functions, caching, timing, logging, validation wrappers.
For performance work: measure before changing, profile to find bottlenecks, compare before and after.
For ordered processing: A* search, Dijkstra, event simulation, task scheduling. Efficient min/max extraction with heap-based queue.
For dynamic programming: overlapping subproblems, recursive solutions with repeated computations, memoization to avoid redundant work.
For persistent state: closures capture outer variables, alternative to classes for simple state, factory functions that remember context.
| name | build-expression-tree |
| description | For symbolic computation: ASTs, mathematical expressions, code that manipulates code structure, expression transformations. |
Represent expressions as nested data structures (tuples, classes, or trees).
# Tuple representation
expr = ('+', ('*', 'x', 2), 1) # (x * 2) + 1
# Class representation
class Expr:
def __init__(self, op, *args):
self.op, self.args = op, args
def __add__(self, other):
return Expr('+', self, other)
def __mul__(self, other):
return Expr('*', self, other)
x = Expr('x')
expr = x * 2 + 1 # Builds expression tree
# Recursive evaluation
def evaluate(expr, env):
if isinstance(expr, str):
return env[expr] # Variable lookup
if isinstance(expr, (int, float)):
return expr
op, *args = expr if isinstance(expr, tuple) else (expr.op, *expr.args)
values = [evaluate(a, env) for a in args]
return {'+': lambda a,b: a+b, '*': lambda a,b: a*b}[op](*values)
class Expression:
"""A symbolic mathematical expression."""
def __init__(self, op, *args):
self.op, self.args = op, args
def __add__(self, other): return Expression('+', self, other)
def __radd__(self, other): return Expression('+', other, self)
def __mul__(self, other): return Expression('*', self, other)
def __rmul__(self, other): return Expression('*', other, self)
def __neg__(self): return Expression('-', self)
def __repr__(self):
if len(self.args) == 1:
return f"({self.op}{self.args[0]})"
return f"({self.args[0]} {self.op} {self.args[1]})"
class Function(Expression):
"""A function like sin or cos."""
def __call__(self, x):
return Expression(self, x)
# Create symbols and functions
x = Expression('x')
sin, cos = Function('sin'), Function('cos')
# Build expressions naturally
expr = sin(x) + cos(x) * 2
# Expression tree: (+ (sin x) (* (cos x) 2))
# Symbolic differentiation
def D(y, x=x):
"""Differentiate y with respect to x."""
if y == x: return 1
if not isinstance(y, Expression): return 0
op, args = y.op, y.args
if op == '+': return D(args[0], x) + D(args[1], x)
if op == '*': return D(args[0], x) * args[1] + args[0] * D(args[1], x)
if op == sin: return cos(args[0]) * D(args[0], x)
# ... more rules
2 + x not just x + 20 + x to x, etc.